A note on Sugeno exponential function with respect to distortion

Shekhar Singh Negi and Vicenç Torra

Applied Mathematics and Computation, 2024, vol. 470, issue C

Abstract: This study explores the Sugeno exponential function, which is the solution to a first order differential equation with respect to nonadditive measures, specifically distorted Lebesgue measures. We define k-distorted semigroup property of the Sugeno exponential function, introduce a new addition operation on a set of distortion functions, and discuss some related results. Furthermore, m-Bernoulli inequality, a more general inequality than the well-known Bernoulli inequality on the real line, is established for the Sugeno exponential function. Additionally, the above concept is extended to a system of differential equations with respect to the distorted Lebesgue measure which gives rise to the study of a matrix m-exponential function.

Keywords: Nonadditive measure; Semigroup theory; Banach space; Choquet integral; Bernoulli inequality; Time scale theory (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:470:y:2024:i:c:s0096300324000584

DOI: 10.1016/j.amc.2024.128586

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